Mollweide's formula

In trigonometry, Mollweide's formula, sometimes referred to in older texts as Mollweide's equations, named after Karl Mollweide, is a set of two relationships between sides and angles in a triangle.

It can be used to check solutions of triangles.

Let a, b, and c be the lengths of the three sides of a triangle. Let α, β, and γ be the measures of the angles opposite those three sides respectively. Mollweide's formula states that

and

Each of these identities uses all six parts of the triangle—the three angles and the lengths of the three sides.